We start with a special situation where both the local QFT and the boundary/defect are integrable. The reason is that the \(T\bar{T}\)  deformation preserves integrability and as a result, such theories can be studied by the powerful toolkit of integrable models, in particular employing the scattering picture and factorized S-matrices. Such a description is very convenient for the study of the \(T\bar{T}\)  deformed integrable QFTs because the bulk S-matrix is deformed in a simple way [1]}, [2]}, [3]}. The new ingredients in the boundary/defect case are the deformed boundary and defect S-matrices, which will be derived along the lines of [4]}, [5]}, [6]}. Once the deformed S-matrices are known, we can apply the machinery of integrability to compute various important physical quantities. This procedure is universal and does not depend on details of the theory under consideration. In this sense, the deformed quantum model is more straightforward to study than the classical counterpart.
